Developments in Reliable Computing

The SCAN conference, the International Symposium on Scientific Com­ puting, Computer Arithmetic and Validated Numerics, takes place bian­ nually under the joint auspices of GAMM (Gesellschaft fiir Angewandte Mathematik und Mechanik) and IMACS (International Association for Mathematics and Computers in Simulation). SCAN-98 attracted more than 100 participants from 21 countries all over the world. During the four days from September 22 to 25, nine highlighted, plenary lectures and over 70 contributed talks were given. These figures indicate a large participation, which was partly caused by the attraction of the organizing country, Hungary, but also the effec­ tive support system have contributed to the success. The conference was substantially supported by the Hungarian Research Fund OTKA, GAMM, the National Technology Development Board OMFB and by the J6zsef Attila University. Due to this funding, it was possible to subsidize the participation of over 20 scientists, mainly from Eastern European countries. It is important that the possibly first participation of 6 young researchers was made possible due to the obtained support. The number of East-European participants was relatively high. These results are especially valuable, since in contrast to the usual 2 years period, the present meeting was organized just one year after the last SCAN-xx conference. Front Matter....Pages i-viii Rigorous Global Search: Industrial Applications....Pages 1-16 Influences of Rounding Errors in Solving Large Sparse Linear Systems....Pages 17-30 A Hardware Approach to Interval Arithmetic for Sine and Cosine Functions....Pages 31-41 Towards an optimal control of the wrapping effect....Pages 43-51 On Existence and Uniqueness of Solutions of Linear Algebraic Equations in Kaucher’s Interval Arithmetic....Pages 53-65 A Comparison of Subdivision Strategies for Verified Multi-Dimensional Gaussian Quadrature....Pages 67-75 INTLAB — INTerval LABoratory....Pages 77-104 Verified calculation of the solution of algebraic Riccati equation....Pages 105-118 Expression Concepts in Scientific Computing....Pages 119-130 Performance Evaluation Technique STU and libavi Library....Pages 131-140 Single-Number Interval I/O....Pages 141-148 Interval Analysis for Embedded Systems....Pages 149-158 Prediction by extrapolation for interval tightening methods....Pages 159-166 The Contribution of T. Sunaga to Interval Analysis and Reliable Computing....Pages 167-188 Surface-to-surface intersection with complete and guaranteed results....Pages 189-202 An Algorithm that Computes a Lower Bound on the Distance Between a Segment and Z 2 ....Pages 203-212 Comparing Partial Consistencies....Pages 213-228 Verified Computation of Fast Decreasing Polynomials....Pages 229-240 An Accurate Distance-Calculation Algorithm for Convex Polyhedra....Pages 241-253 Verified Error Bounds for Linear Systems Through the Lanczos Process....Pages 255-267 A Representation of the Interval Hull of a Tolerance Polyhedron Describing Inclusions of Function Values and Slopes....Pages 269-278 A Few Results on Table-Based Methods....Pages 279-288 An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation....Pages 289-310 The Interval-Enhanced GNU Fortran Compiler....Pages 311-322 Outer Estimation of Generalized Solution Sets to Interval Linear Systems....Pages 323-335 A Real Polynomial Decision Algorithm Using Arbitrary-Precision Floating Point Arithmetic....Pages 337-346 A Numerical Verification Method of Solutions for the Navier-Stokes Equations....Pages 347-357 Convex Sets of Full Rank Matrices....Pages 359-364 Multiaspect Interval Types....Pages 365-372 MATLAB-Based Analysis of Roundoff Noise....Pages 373-382 SCAN-98 Collected Bibliography....Pages 383-402 The present volume contains 30 articles presented at SCAN-98, Budapest, Hungary. These papers cover all aspects of validation techniques in scientific computing, ranging from hardware requirements, elementary operations, high accuracy function evaluations and interval arithmetic to advanced validating techniques and applications in various fields of practical interest. Audience: This book is of interest to researchers and graduate students whose work involves validation techniques in scientific computing.